Here is a (hopefully correct) array of the 4D Levi-Civita symbol.

(define ε
   #a i32 ((1 4) (1 4) (1 4) (1 4))
     ;; ε_1ABC
    ((((0 0 0 0) (0 0 0 0) (0 0 0 0) (0 0 0 0))  ; ε_11BC
      ((0 0 0 0) (0 0 0 0) (0 0 0 1) (0 0 -1 0)) ; ε_12BC
      ((0 0 0 0) (0 0 0 -1) (0 0 0 0) (0 1 0 0)) ; ε_13BC
      ((0 0 0 0) (0 0 1 0) (0 -1 0 0) (0 0 0 0))) ; ε_14BC
     ;; ε_2ABC
     (((0 0 0 0) (0 0 0 0) (0 0 0 -1) (0 0 1 0)) ; ε_21BC
      ((0 0 0 0) (0 0 0 0) (0 0 0 0) (0 0 0 0))  ; ε_22BC
      ((0 0 0 1) (0 0 0 0) (0 0 0 0) (-1 0 0 0)) ; ε_23BC
      ((0 0 1 0) (0 0 0 0) (-1 0 0 0) (0 0 0 0))) ; ε_24BC
     ;; ε_3ABC
     (((0 0 0 0) (0 0 0 -1) (0 0 0 0) (0 1 0 0)) ; ε_31BC
      ((0 0 0 -1) (0 0 0 0) (0 0 0 0) (1 0 0 0)) ; ε_32BC
      ((0 0 0 0) (0 0 0 0) (0 0 0 0) (0 0 0 0)) ; ε_33BC
      ((0 1 0 0) (-1 0 0 0) (0 0 0 0) (0 0 0 0))) ; ε_34BC
     ;; ε_4ABC
     (((0 0 0 0) (0 0 -1 0) (0 1 0 0) (0 0 0 0)) ; ε_41BC
      ((0 0 -1 0) (0 0 0 0) (1 0 0 0) (0 0 0 0)) ; ε_42BC
      ((0 1 0 0) (-1 0 0 0) (0 0 0 0) (0 0 0 0)) ; ε_43BC
      ((0 0 0 0) (0 0 0 0) (0 0 0 0) (0 0 0 0)))) ; ε44BC
)

(The Levi-Civita symbol is defined where ε_ABCD = 1 if (A,B,C,D) is an
even permutation of (1,2,3,4), -1 if it is odd, and zero if it is
neither. So it is a better candidate for a generalized array instead of
a specialized array. But it is a real example.)

On 4/11/26 21:55, John Cowan wrote:
> I haven't been able to find a compelling example of a 4-D array.
> There is a synthetic example of a 3-D array in the format-array
> section.